I agree with you.. to a point. I understand that when you're suicidal yourself it can seem like the best advice you can give another suicidal person is to go through with it. You've already established in your mind that it is a viable solution and quite likely also that the world is a shitty place not worth living in. If the person's life/situation seems shitty on top of that and you don't see a way it could improve then the most honest advice (from your perspective) could well be to commit suicide. But I don't think it actually works that way most of the time. Depressed people are not crazy and are able to think rationally despite the illness, especially if it's about someone else. They know that suicide is bad and the right thing to do is to try and prevent it, not encourage it. They are also just like everyone else in that they want good things for the people they care about and generally would rather not have them die.

In any case, a depressed, suicidal person would be able to make the decision "do the right thing" (and know what the right thing is!) and try and help or at least not encourage another person to commit suicide. Depression and suicidal ideation can fuck with people a lot, but it doesn't take away their sense of right and wrong or their ability to be in control of their actions (for the most part). I can see a depressed person maybe not immediately shutting down someone who mentions wanting to kill themselves, but to encourage it and push them towards it or even directly tell them to take the necessary steps to complete the suicide ("Jump from that bridge", "Get back in") is a whole different level and no amount of depression or suicidal thoughts would make someone do that. She might have been depressed, but she did what she did for another reason.